Stability analysis with applications of a two-dimensional dynamical system arising from a stochastic model of an asset market

TL;DR

This paper investigates the stability and periodicity of a two-dimensional dynamical system modeling asset prices and demand, derived from a heterogeneous agent market model, to explain market fluctuations.

Contribution

It introduces a novel two-dimensional dynamical system based on a microscopic agent model, enabling analysis of market phenomena at a macroscopic level.

Findings

Identifies conditions for stability and periodicity of the system.

Links model parameters to real market fluctuations.

Provides insights into causes of price and demand variability.

Abstract

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system's parameters correspond to: (a) the proportion of speculators in a market; (b) the traders' speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset's fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study two-dimensional dynamical systems and apply them for explanation of socio-economic phenomena.